Re: should the default be lower bounds or upper bounds?
Peter McGoron 12 Apr 2026 03:17 UTC
Here is a (hopefully correct) array of the 4D Levi-Civita symbol.
(define ε
#a i32 ((1 4) (1 4) (1 4) (1 4))
;; ε_1ABC
((((0 0 0 0) (0 0 0 0) (0 0 0 0) (0 0 0 0)) ; ε_11BC
((0 0 0 0) (0 0 0 0) (0 0 0 1) (0 0 -1 0)) ; ε_12BC
((0 0 0 0) (0 0 0 -1) (0 0 0 0) (0 1 0 0)) ; ε_13BC
((0 0 0 0) (0 0 1 0) (0 -1 0 0) (0 0 0 0))) ; ε_14BC
;; ε_2ABC
(((0 0 0 0) (0 0 0 0) (0 0 0 -1) (0 0 1 0)) ; ε_21BC
((0 0 0 0) (0 0 0 0) (0 0 0 0) (0 0 0 0)) ; ε_22BC
((0 0 0 1) (0 0 0 0) (0 0 0 0) (-1 0 0 0)) ; ε_23BC
((0 0 1 0) (0 0 0 0) (-1 0 0 0) (0 0 0 0))) ; ε_24BC
;; ε_3ABC
(((0 0 0 0) (0 0 0 -1) (0 0 0 0) (0 1 0 0)) ; ε_31BC
((0 0 0 -1) (0 0 0 0) (0 0 0 0) (1 0 0 0)) ; ε_32BC
((0 0 0 0) (0 0 0 0) (0 0 0 0) (0 0 0 0)) ; ε_33BC
((0 1 0 0) (-1 0 0 0) (0 0 0 0) (0 0 0 0))) ; ε_34BC
;; ε_4ABC
(((0 0 0 0) (0 0 -1 0) (0 1 0 0) (0 0 0 0)) ; ε_41BC
((0 0 -1 0) (0 0 0 0) (1 0 0 0) (0 0 0 0)) ; ε_42BC
((0 1 0 0) (-1 0 0 0) (0 0 0 0) (0 0 0 0)) ; ε_43BC
((0 0 0 0) (0 0 0 0) (0 0 0 0) (0 0 0 0)))) ; ε44BC
)
(The Levi-Civita symbol is defined where ε_ABCD = 1 if (A,B,C,D) is an
even permutation of (1,2,3,4), -1 if it is odd, and zero if it is
neither. So it is a better candidate for a generalized array instead of
a specialized array. But it is a real example.)
On 4/11/26 21:55, John Cowan wrote:
> I haven't been able to find a compelling example of a 4-D array.
> There is a synthetic example of a 3-D array in the format-array
> section.